Please choose the letter corresponding to the best answer to each problem (5 pts each). 1. A 10-m uniform horizontal beam of weight 75 N is supported by two vertical posts. The left post is at the left end of beam while the right post is 2.0 m from the right end of the beam. If a 400-N person sits at 1.5 m from the left end of the beam, what is the force of the beam on the right post? (A) 47 N (B) 75 N (C) 98 N (D) 240 N (E) 120 N 2. A passenger van has an outer wheel base width of 2.00 m. Its center of gravity is equidistant from the sides, and positioned 1.20 m above the ground. What is the maximum sideways angle at which it can be inclined without tipping over? (A) 32.6 (B) 33.6 (C) 39.8 (D) 50.2 (E) 56.4 3. A uniform solid sphere has mass M and radius R. If the mass is decreased to 1 M and the radius is 3 increased to 2R, what happens to the sphere's moment of inertia about an axis passing through the center of the sphere? (A) Decreases by a factor of 0.22 (B) Decreases by a factor of 0.44 (C) Decreases by a factor of 0.75 (D) Increases by a factor of 1.3 (E) Increases by a factor of 1.5 4. A solid cylinder is mounted on a horizontal frictionless axle through the axis of the cylinder. Its moment of inertia is 13.5 kg m 2. A rope, wrapped around the outer radius R 1 =1:5 m, exerts a force F 1 =6:0 N to the right. A second rope wrapped around another section of radius R 2 =0:50 m exerts a force F 2 =6:0 Ndownward. What is the angular acceleration of the cylinder (magnitude and direction)? (A) 0.88 rad/s 2 clockwise (B) 0.88 rad/s 2 counter clockwise (C) 0.44 rad/s 2 clockwise (D) 0.44 rad/s 2 counter clockwise (E) Since the net force is zero, the angular acceleration is zero. 1
5. A proton of mass 1:67 10 ;27 kg rotates with an angular speed 2 10 6 rad/s in a circle of radius 0.80 m in a cyclotron. What is the angular momentum of the proton in its circular motion? (A) 1:28 10 ;21 kg m 2 /s (B) 1:76 10 ;21 kg m 2 /s (C) 2:14 10 ;21 kg m 2 /s (D) 2:98 10 ;21 kg m 2 /s (E) 3:24 10 ;21 kg m 2 /s 6. A man of mass 75.0 kg stands on the edge of a horizontal rotating circular disk (turntable) of radius 5.00 m. The disk alone (without the man) has a moment of inertia of 3:13 10 3 kg m 2. The disk with man is rotating with an angular velocity of 1.50 rad/s, with negligible friction, and is coasting with no external torque. What is the angular velocity of the disk if the man moves 3.00 m toward the center of the disk (i.e. the man is 2.00 m from the center of the turntable)? (A) 2.19 rad/s. (B) 1.97 rad/s. (C) 1.14 rad/s. (D) 1.03 rad/s. (E) The angular velocity does not change. 7. An aluminum wire is 2.0 m in length with a cross-sectional area of 3:14 10 ;6 m 2. A 10.0 kg mass is hanging from the wire. What is the elongation of the wire due to the mass? (The elastic modulus for aluminum is 7:0 10 10 N/m 2 ) (A) 0.11 mm (B) 0.22 mm (C) 0.32 mm (D) 0.43 mm (E) 0.89 mm 8. A 500 N weight sits on the small piston of a hydraulic machine. The small piston has area 2.0 cm 2. If the large piston has area 40 cm 2,howmuch weight can the large piston support? (A) 25 N (B) 500 N (C) 5000 N (D) 10000 N (E) 20000 N 2
9. An ideal uid ows with incompressible steady-state ow at 12 m/s in a horizontal pipe. If the pipe narrows to half its original radius, what is the ow speed in the narrower section? (A) 3.0 m/s (B) 12 m/s (C) 24 m/s (D) 36 m/s (E) 48 m/s 10. A hurricane force wind (horizontal) of 45 m/s blows over a at horizontal roof of dimensions 20.0 m by 25.0 m. What is the lift force on the roof due to the wind? The density of air is 1.29 kg/m 3. (A) 6:5 10 5 N (B) 1:3 10 6 N (C) 14 N (D) 2:9 10 4 N (E) 2:0 10 5 N 11. Salt water has greater density than fresh water. A boat oats in both fresh water and in salt water. Where is the buoyant force greater on the boat? (A) Salt water. (B) Fresh water. (C) Buoyant force is the same in both. (D) The buoyant force is equal to the atmospheric pressure times the surface area of the boat. (E) Impossible to determine from the information given. 12. How much gauge pressure must a submarine be able to withstand at a depth of 120 m in sea water? (We assume that the interior of the submarine maintains a pressure of 1 atm.) (A) 0:986 10 6 Pa (B) 1:06 10 6 Pa (C) 1:11 10 6 Pa (D) 1:21 10 6 Pa (E) 1:31 10 6 Pa 3
13. A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane without slipping. How fast is it moving after the center of mass has dropped a vertical distance of 3.0 m? (A) 1.6 m/s (B) 2.2 m/s (C) 3.8 m/s (D) 5.4 m/s (E) 7.7 m/s 14. A 500 meter long steel arch bridge experiences temperature extremes of -20 o Cand35 o C. For steel, =11 10 ;6 = o CHowmuch will its length change between these two extremes? (A) 11 cm (B) 19 cm (C) 30 cm (D) 42 cm (E) 51 cm 15. A sample of a monatomic ideal gas is originally at 20 o C. What is the nal temperature of the gas if both the pressure and volume are doubled? (A) 5 o C (B) 20 o C (C) 80 o C (D) 900 o C (E) 1200 o C 16. A granite wall has a thickness of 0.61 m and a thermal conductivityof2.1w=(m o C). The temperature on one face of the wall is 3.2 C and 20.0 C on the opposite face. How much heat is transferred in one hour through each square meter of the granite wall? (A) 210 000 J=m 2 (B) 106 000 J=m 2 (C) 77 000 J=m 2 (D) 1800 J=m 2 (E) 58 J=m 2 4
17. A 0.040-kg ice cube at 0 o C is placed in an insulated box that contains 0.0075 kg of steam at 100 o C. What is the equilibrium temperature reached by this closed system? (Assume that all of the ice melts. For water, L f =3:33 10 5 J=kg, L v =2:26 10 6 J=kg.) (A) 22.7 o C (B) 33.6 o C (C) 44.9 o C (D) 50.7 o C (E) 66.4 o C 18. A beaker of water is placed on a Bunsen burner. As the lower layers of water are heated, they become less dense and rise. This permits cooler layers to move downward and be heated. Eventually, the water boils. Which method(s) of heat transfer is (are) primarily responsible for boiling the sample? (A) conduction (B) convection (C) radiation (D) both conduction and radiation (E) both conduction and convection 19. What is the average kinetic energy of oxegen molecules at a temperature of 300 K? (A) 12:4 10 ;21 J (B) 2:07 10 ;21 J (C) 6:21 10 ;21 J (D) 6:21 10 21 J (E) 2:07 10 ;23 J 20. A class of 10 students taking an exam has a power output per student of about 200 W. Assume that the initial temperature of the room is 20 o C and that its dimensions are 6.0 m by 15.0mby3.0m. What is the temperature of the room at then of 1.0 h if all the heat remains in the air in the room and none is added by an outside source? The specic heat of air is 837 J/kg o C, and its density is about 1:3 10 ;3 g/cm 3. (A) 21 o C (B) 22 o C (C) 25 o C (D) 45 o C (E) 50 o C 5